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Original
2026-01-01
Modified
2026-02-21
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<p>100 100 can be easily converted from decimal to binary.</p>
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<p>100 100 can be easily converted from decimal to binary.</p>
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<p>The methods outlined below will assist in this conversion. Let’s explore the process.</p>
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<p>The methods outlined below will assist in this conversion. Let’s explore the process.</p>
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<p><strong>Expansion Method</strong>: Here is the step-by-step process of converting 100 100 using the expansion method.</p>
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<p><strong>Expansion Method</strong>: Here is the step-by-step process of converting 100 100 using the expansion method.</p>
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<p><strong>Step 1</strong>- Determine the place values: In the binary system, each<a>place value</a>is a<a>power</a>of 2. Therefore, we will ascertain the powers of 2.</p>
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<p><strong>Step 1</strong>- Determine the place values: In the binary system, each<a>place value</a>is a<a>power</a>of 2. Therefore, we will ascertain the powers of 2.</p>
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<p>20 = 1,</p>
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<p>20 = 1,</p>
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<p>21 = 2,</p>
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<p>21 = 2,</p>
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<p>22 = 4,</p>
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<p>22 = 4,</p>
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<p>23 = 8,</p>
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<p>23 = 8,</p>
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<p>24 = 16,</p>
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<p>24 = 16,</p>
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<p>25 = 32,</p>
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<p>25 = 32,</p>
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<p>26 = 64,</p>
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<p>26 = 64,</p>
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<p>27 = 128,</p>
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<p>27 = 128,</p>
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<p>28 = 256,</p>
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<p>28 = 256,</p>
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<p>29 = 512,</p>
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<p>29 = 512,</p>
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<p>210 = 1024,</p>
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<p>210 = 1024,</p>
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<p>211 = 2048,</p>
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<p>211 = 2048,</p>
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<p>212 = 4096,</p>
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<p>212 = 4096,</p>
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<p>213 = 8192,</p>
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<p>213 = 8192,</p>
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<p>214 = 16384,</p>
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<p>214 = 16384,</p>
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<p>215 = 32768,</p>
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<p>215 = 32768,</p>
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<p>216 = 65536,</p>
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<p>216 = 65536,</p>
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<p>Since 65536 is<a>less than</a>100 100, we use up to 216.</p>
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<p>Since 65536 is<a>less than</a>100 100, we use up to 216.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In this step, identify the largest power of 2 that is less than or equal to 100 100.</p>
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<p><strong>Step 2</strong>- Identify the largest power of 2: In this step, identify the largest power of 2 that is less than or equal to 100 100.</p>
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<p>Since 216 = 65536 is the number we are looking for, write 1 in the 216 place. Now, subtract 65536 from 100 100. 100 100 - 65536 = 34564.</p>
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<p>Since 216 = 65536 is the number we are looking for, write 1 in the 216 place. Now, subtract 65536 from 100 100. 100 100 - 65536 = 34564.</p>
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<p><strong>Step 3</strong>- Identify the next largest power of 2: Find the largest power of 2 that fits into 34564.</p>
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<p><strong>Step 3</strong>- Identify the next largest power of 2: Find the largest power of 2 that fits into 34564.</p>
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<p>The next largest power is 215 = 32768. Now, write 1 in the 215 place and subtract 32768 from 34564. 34564 - 32768 = 1796.</p>
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<p>The next largest power is 215 = 32768. Now, write 1 in the 215 place and subtract 32768 from 34564. 34564 - 32768 = 1796.</p>
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<p><strong>Step 4</strong>- Continue the process until the<a>remainder</a>is 0.</p>
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<p><strong>Step 4</strong>- Continue the process until the<a>remainder</a>is 0.</p>
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<p><strong>Step 5</strong>- Identify the unused place values: Write 0s in the remaining places.</p>
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<p><strong>Step 5</strong>- Identify the unused place values: Write 0s in the remaining places.</p>
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<p><strong>Step 6</strong>- Write the values in reverse order to represent 100 100 in binary.</p>
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<p><strong>Step 6</strong>- Write the values in reverse order to represent 100 100 in binary.</p>
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<p><strong>Grouping Method</strong>: This method involves dividing 100 100 by 2. Let’s see the step-by-step conversion.</p>
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<p><strong>Grouping Method</strong>: This method involves dividing 100 100 by 2. Let’s see the step-by-step conversion.</p>
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<p><strong>Step 1</strong>- Divide the given number 100 100 by 2.</p>
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<p><strong>Step 1</strong>- Divide the given number 100 100 by 2.</p>
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<p><strong>Step 2</strong>- The quotient becomes the new dividend. Continue dividing by 2 until the quotient is 0.</p>
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<p><strong>Step 2</strong>- The quotient becomes the new dividend. Continue dividing by 2 until the quotient is 0.</p>
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<p><strong>Step 3</strong>- Write down the remainders from bottom to top. Therefore, 100 100 (decimal) = 110000110100 (binary).</p>
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<p><strong>Step 3</strong>- Write down the remainders from bottom to top. Therefore, 100 100 (decimal) = 110000110100 (binary).</p>
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